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Wolfram Language & System Documentation Center
QuantityVariableDimensions
  • See Also
    • QuantityVariable
    • QuantityVariablePhysicalQuantity
    • QuantityVariableCanonicalUnit
    • NondimensionalizationTransform
  • Related Guides
    • Units & Quantities
    • Formulas
    • See Also
      • QuantityVariable
      • QuantityVariablePhysicalQuantity
      • QuantityVariableCanonicalUnit
      • NondimensionalizationTransform
    • Related Guides
      • Units & Quantities
      • Formulas

QuantityVariableDimensions[quantityvariable]

returns a list of base dimensions associated with the specified quantityvariable.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • QuantityVariable
    • QuantityVariablePhysicalQuantity
    • QuantityVariableCanonicalUnit
    • NondimensionalizationTransform
  • Related Guides
    • Units & Quantities
    • Formulas
    • See Also
      • QuantityVariable
      • QuantityVariablePhysicalQuantity
      • QuantityVariableCanonicalUnit
      • NondimensionalizationTransform
    • Related Guides
      • Units & Quantities
      • Formulas

QuantityVariableDimensions

QuantityVariableDimensions[quantityvariable]

returns a list of base dimensions associated with the specified quantityvariable.

Details

  • QuantityVariableDimensions returns a list of ordered dimension pairs, indicating the magnitude of the quantityvariable in that physical dimension.
  • quantityvariable can be a QuantityVariable, a combination of QuantityVariable objects, or the Derivative of a QuantityVariable. quantityvariable can also include "PhysicalQuantity" entities.
  • Physical dimensions include: "AmountUnit", "AngleUnit", "ElectricCurrentUnit", "InformationUnit", "LengthUnit", "LuminousIntensityUnit", "MassUnit", "MoneyUnit", "SolidAngleUnit", "TemperatureDifferenceUnit", "TemperatureUnit", and "TimeUnit".
  • Electromagnetic dimensions follow the SI convention.

Examples

open all close all

Basic Examples  (2)

Find the physical dimensions of a QuantityVariable:

Use the single-argument form of QuantityVariable:

Scope  (3)

Find the physical dimensions of a combination of QuantityVariable objects:

Determine the physical dimensions of the Derivative of a QuantityVariable:

Discover the dimensions of an arbitrary combination of QuantityVariable objects and their derivatives:

Applications  (2)

Find the dimensional coefficients of a sampling of electrical physical quantities:

Check equations for dimensional consistency:

Define the variables in a standard format based on their dimensions:

Check that the formula is dimensionally correct:

Properties & Relations  (2)

The dimensions of "PhysicalQuantity" entities can also be determined:

Use the ResourceFunction "PhysicalQuantityLookup" to find physical quantities from unit dimensions:

Possible Issues  (2)

Some physical quantities are dimensionless:

For functions of QuantityVariable, dimensions are only returned for the head:

Find the dimensions of derivatives:

Neat Examples  (2)

Explore the space of common physical quantities of mechanics:

Estimating the power of a bomb blast based on dimensional analysis, using only these physical quantities:

Find the dimensions of these physical quantities:

Write dimensional equations for the physical quantities involved:

Make an ansatz for the energy as a function of radius, mass, time, and mass density:

Form and solve linear equations for the exponents:

Given the inputs of the parameters at a given time, estimate the energy of an explosion:

See Also

QuantityVariable  QuantityVariablePhysicalQuantity  QuantityVariableCanonicalUnit  NondimensionalizationTransform

Related Guides

    ▪
  • Units & Quantities
  • ▪
  • Formulas

History

Introduced in 2014 (10.0) | Updated in 2018 (11.3)

Wolfram Research (2014), QuantityVariableDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html (updated 2018).

Text

Wolfram Research (2014), QuantityVariableDimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html (updated 2018).

CMS

Wolfram Language. 2014. "QuantityVariableDimensions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html.

APA

Wolfram Language. (2014). QuantityVariableDimensions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html

BibTeX

@misc{reference.wolfram_2025_quantityvariabledimensions, author="Wolfram Research", title="{QuantityVariableDimensions}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}", note=[Accessed: 01-June-2026]}

BibLaTeX

@online{reference.wolfram_2025_quantityvariabledimensions, organization={Wolfram Research}, title={QuantityVariableDimensions}, year={2018}, url={https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html}, note=[Accessed: 01-June-2026]}

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